Apparatus for measuring ammonia concentration, system for measuring ammonia concentration, system for treating exhaust gas, and method for measuring ammonia concentration

ABSTRACT

An apparatus for measuring ammonia concentration measures ammonia concentration in a target gas with a sensor element including a mixed potential cell. The apparatus for measuring ammonia concentration includes an electromotive force acquisition section, an oxygen concentration acquisition section, and an ammonia concentration derivation section. The ammonia concentration derivation section derives the ammonia concentration in the target gas from the relationship represented by formula (1): 
       EMF=α log a ( p   NH3 )−β log b ( p   O2 )+γ log c ( p   NH3 )×log d ( p   O2 )+ B   (1)
     (where   EMF: an electromotive force of the mixed potential cell,   α, β, γ, and B: constants (provided that each of α, β, and γ≠0),   a, b, c, and d: any base (provided that each of a, b, c, and d≠1, and each of a, b, c, and d&gt;0),   p NH3 : the ammonia concentration in the target gas, and   p O2 : the oxygen concentration in the target gas).

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to an apparatus for measuring ammoniaconcentration, a system for measuring ammonia concentration, a systemfor treating an exhaust gas, and a method for measuring ammoniaconcentration.

2. Description of the Related Art

Hitherto, ammonia sensors to detect ammonia concentrations in targetgases such as exhaust gases of automobiles have been known. For example,Patent Literature 1 describes a multi-gas sensor including an ammoniasensing section having a pair of electrodes arranged on a solidelectrolyte body. Formula (2) based on a mixed-potential formula isknown as the characteristics of the electromotive force (EMF) of a mixedpotential cell including solid electrolyte body and a pair of electrodes(for example, Non-Patent Literature 1).

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 1} \rbrack & \; \\{{EMF} \propto {\frac{RT}{2F}( {{\frac{2}{3}\ln \; p_{{NH}\; 3}} - {\frac{1}{2}\ln \; p_{O\; 2}} - {\ln \; p_{H\; 2O}}} )}} & (2)\end{matrix}$

(where

EMF: the electromotive force of the mixed potential cell

R: a gas constant [J/(K·mol)]

T: the temperature of the mixed potential cell [K]

F: the Faraday constant [C/mol]

p_(NH3): ammonia concentration in a target gas

p_(O2): oxygen concentration in the target gas

p_(H2O): H₂O concentration in the target gas)

CITATION LIST Patent Literature

[PTL 1] Japanese Patent No. 5204160

Non Patent Literature

[NPL 1] D. Schonauer et al., Sensors and Actuators B vol. 140(2009), p.585-590

SUMMARY OF THE INVENTION

However, the inventors have conducted studies and have found that inactual sensor elements, the relationship among an electromotive forceEMF, ammonia concentration p_(NH3), oxygen concentration p_(O2), H₂Oconcentration p_(H2O) does not obey formula (2), in some cases. Thus,when the ammonia concentration p_(NH3) is calculated from formula (2) ina mixed potential-type ammonia sensor, the ammonia concentration in thetarget gas is not accurately derived, in some cases.

The present invention has been accomplished in order to solve theseproblems and mainly aims to derive ammonia concentration in a target gaswith higher accuracy.

In the present invention, the following measures are used in order toachieve the above-described main object.

An apparatus of the present invention for measuring ammoniaconcentration in a target gas with a sensor element including a mixedpotential cell that includes a solid electrolyte body, a detectionelectrode arranged on the solid electrolyte body, and a referenceelectrode arranged on the solid electrolyte body, includes:

an electromotive force acquisition section configured to acquireinformation about an electromotive force of the mixed potential cellwhile the detection electrode is exposed to the target gas;

an oxygen concentration acquisition section configured to acquireinformation about oxygen concentration in the target gas; and

an ammonia concentration derivation section configured to derive ammoniaconcentration in the target gas from the acquired information about theelectromotive force, the acquired information about the oxygenconcentration, and the relationship represented by formula (1):

EMF=α log_(a)(p _(NH3))−β log_(b)(p _(O2))+γ log_(c)(p _(NH3))×log_(d)(p_(O2))+B  (1)

(where

-   EMF: an electromotive force of the mixed potential cell,-   α, β, γ, and B: constants (provided that each of α, β, and γ≠0),-   a, b, c, and d: any base (provided that each of a, b, c, and-   d≠1, and each of a, b, c, and d>0),-   p_(NH3): the ammonia concentration in the target gas, and-   p_(O2): the oxygen concentration in the target gas).

In the apparatus for measuring ammonia concentration, the ammoniaconcentration in the target gas is derived from the information aboutthe electromotive force of the mixed potential cell of the sensorelement, the information about the oxygen concentration in the targetgas, and the relationship of formula (1). In this way, the use offormula (1) can derive the ammonia concentration in the target gas withhigher accuracy than that in the case of using formula (2) describedabove. Here, the derivation of the ammonia concentration on the basis ofthe relationship of formula (1) may be performed by using therelationship of formula (1) and is not limited to the derivation of theammonia concentration using formula (1) itself. For example, the ammoniaconcentration may be derived from a formula obtained by modifyingformula (1). The relationship among the values of the variables (EMF,p_(NH3), p_(O2)) of formula (1) is stored in the form of a map, and theammonia concentration may be derived from the map. The constants α, β,and B are values depending on the sensor element and can be determinedby, for example, experiments in advance.

In this case, the target gas may have a temperature of 150° C. orhigher. The target gas may have a 200° C. or higher. The target gas mayhave a temperature of 400° C. or lower.

A system of the present invention for measuring ammonia concentrationincludes the sensor element and the ammonia concentration measurementapparatus. Accordingly, the system for measuring ammonia concentrationhas the same effect as the apparatus of the present invention formeasuring ammonia concentration, i.e., for example, the effect ofderiving ammonia concentration in a target gas with higher accuracy.

In the system for measuring ammonia concentration, the detectionelectrode may be composed of a Au—Pt alloy as a main component. TheAu—Pt alloy is suitable for a main component of the detection electrodebecause a mixed potential is easily established at the triple phaseboundary of the solid electrolyte body and the target gas. In this case,the detection electrode may have a degree of concentration (=amount ofAu present [atom %]/amount of Pt present [atom %]) of 0.3 or more, thedegree of concentration being measured by at least one of X-rayphotoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES).A degree of concentration of 0.3 or more can more reliably establish themixed potential. The degree of concentration may be 0.1 or more.

In the system of the present invention for measuring ammoniaconcentration, the sensor element may include a heater configured toheat the mixed potential cell to an operating temperature of 450° C. orhigher and 650° C. or lower. In the system for measuring ammoniaconcentration, the use of an operating temperature of 450° C. or highercan appropriately activate the solid electrolyte body. In the system formeasuring ammonia concentration, the use of an operating temperature of650° C. or lower can inhibit a decrease in measurement accuracy due tothe combustion of ammonia. The operating temperature may be 600° C. orlower.

A system of the present invention for treating an exhaust gas includesany one of the systems for measuring ammonia concentration according tothe foregoing embodiments, and an exhaust gas path through which anexhaust gas serving as the target gas from an internal combustion engineflows, the sensor element being arranged in the exhaust gas path.Accordingly, the system for treating an exhaust gas has the same effectas the system for measuring ammonia concentration, i.e., for example,the effect of deriving ammonia concentration in a target gas with higheraccuracy.

The system of the present invention for treating an exhaust gas mayfurther include one or more oxidation catalysts arranged in the exhaustgas path, in which the sensor element may be arranged on the downstreamside of the exhaust gas path in contrast to one of the one or moreoxidation catalysts arranged at the upstream end. In this case, thetarget gas in which a component (for example, at least one ofhydrocarbons and carbon monoxide) that is present in the target gas andthat affects the measurement accuracy of the ammonia concentration hasbeen oxidized by the oxidation catalysts reaches the sensor element.Thus, in the system for treating an exhaust gas, the ammoniaconcentration in the target gas can be derived with higher accuracy.

A method of the present invention for measuring ammonia concentration ina target gas with a sensor element including a mixed potential cell thatincludes a solid electrolyte body, a detection electrode arranged on thesolid electrolyte body, and a reference electrode arranged on the solidelectrolyte body, includes:

an electromotive force acquisition step of acquiring information aboutan electromotive force of the mixed potential cell while the detectionelectrode is exposed to the target gas;

an oxygen concentration acquisition step of acquiring information aboutoxygen concentration in the target gas; and

a concentration derivation step of deriving the ammonia concentration inthe target gas from the acquired information about the electromotiveforce, the acquired information about the oxygen concentration, and arelationship represented by formula (1):

EMF=α log_(a)(p _(NH3))−β log_(b)(p _(O2))+γ log_(c)(p _(NH3))×log_(d)(p_(O2))+B  (1)

(where

EMF: an electromotive force of the mixed potential cell,

α, β, γ, and B: constants (provided that each of α, β, and γ≠0),

a, b, c, and d: any base (provided that each of a, b, c, and d≠1, andeach of a, b, c, and d>0),

p_(NH3): the ammonia concentration in the target gas, and

p_(O2): the oxygen concentration in the target gas).

As with the foregoing apparatus for measuring ammonia concentration, theammonia concentration in the target gas can be derived with higheraccuracy from the relationship of formula (1) by the method formeasuring ammonia concentration. In the method for measuring ammoniaconcentration, the apparatus for measuring ammonia concentration, thesystem for measuring ammonia concentration, and the system for treatingan exhaust gas according to various embodiments may be used, and stepsof providing these functions may be added.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an explanatory drawing of a system 2 for treating an exhaustgas of an engine 1.

FIG. 2 is an explanatory drawing of a system 20 for measuring ammoniaconcentration.

FIG. 3 is a flow chart illustrating an example of an ammoniaconcentration derivation routine.

FIG. 4 is a flow chart illustrating an example of a constant derivationprocessing.

FIG. 5 is a graph depicting the relationships between ammoniaconcentrations p_(NH3) [ppm] and electromotive forces EMFs [mV] of asensor element 1.

FIG. 6 is a graph depicting the relationship between the oxygenconcentration p_(O2) and the slope K of the sensor element 1.

FIG. 7 is a graph depicting the relationship between the oxygenconcentration p_(O2) and the intercept L of the sensor element 1.

FIG. 8 is a graph depicting actually measured electromotive forces EMFsof the sensor element 1 and straight lines derived from formula (8).

FIG. 9 is a graph depicting the relationship between the H₂Oconcentration p_(H2O) [%] and the electromotive force EMF [mV] of thesensor element 1.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention will be described below withreference to the drawings. FIG. 1 is an explanatory drawing of a system2 for treating an exhaust gas of an engine 1. FIG. 2 is an explanatorydrawing of a system 20 for measuring ammonia concentration.

The system 2 for treating an exhaust gas is a system for treating anexhaust gas serving as a target gas from the engine 1. In thisembodiment, the engine 1 is a diesel engine. As illustrated in FIG. 1,the system 2 for treating an exhaust gas includes an exhaust gas path 3connected to the engine 1 and the system 20 for measuring ammoniaconcentration including a gas sensor 30 arranged in the exhaust gas path3. In the system 2 for treating an exhaust gas, a diesel oxidationcatalyst (DOC) 4, a diesel particulate filter (DPF) 5, an injector 6, aselective catalytic reduction (SCR) 7, the gas sensor 30, and an ammoniaslip catalyst (ASC) 8 are arranged, in this order, from the upstreamside toward the downstream side of the exhaust gas. The DOC 4 is one ofoxidation catalysts included in the system 2 for treating an exhaust gasand converts HC and CO in the exhaust gas into water and carbon dioxidefor detoxification. The DPF 5 traps PM in the exhaust gas. The injector6 is a device configured to inject at least one of ammonia and asubstance capable of forming ammonia (for example, urea) into an exhaustpipe to supply the at least one of ammonia and the substance to the SCR7. In this embodiment, the injector 6 injects urea, and the injectedurea is hydrolyzed to form ammonia. The SCR 7 decomposes nitrogen oxides(NOx) into harmless N₂ and H₂O by reduction using ammonia supplied fromthe injector 6 into the exhaust pipe. The exhaust gas passing throughthe SCR 7 flows through a pipe 10. The gas sensor 30 is attached to thepipe 10. The ASC 8 is arranged downstream of the pipe 10. The ASC 8 isone of the oxidation catalysts included in the system 2 for treating anexhaust gas and is also referred to as a “downstream DOC” with respectto the DOC 4 (upstream DOC). That is, the system 2 for treating anexhaust gas according to this embodiment includes two oxidationcatalysts: the DOC 4 and the ASC 8. The gas sensor 30 is arrangeddownstream in contrast to the DOC 4 arranged at the upstream end amongone or more oxidation catalysts (two oxidation catalysts in thisembodiment) included in the system 2 for treating an exhaust gas. TheASC 8 decomposes excessive ammonia in the exhaust gas passing throughthe SCR 7 into harmless N₂ and H₂O by oxidation. The exhaust gas passingthrough the ASC 8 is released into, for example, air.

The system 20 for measuring ammonia concentration includes the gassensor 30 and an apparatus 70 for measuring ammonia concentration, theapparatus being electrically connected to the gas sensor 30. The gassensor 30 is an ammonia sensor configured to generate an electricalsignal depending on the concentration of excessive ammonia contained inthe target gas passing through the SCR 7 in the pipe 10. The gas sensor30 also functions as an oxygen sensor configured to generate anelectrical signal depending on the concentration of oxygen in the targetgas and serves as a multi-sensor. The apparatus 70 for measuring ammoniaconcentration derives ammonia concentration in the target gas from theelectrical signal generated by the gas sensor 30 and transmits theresulting data to an engine ECU 9. The engine ECU 9 controls the amountof urea injected from the injector 6 into the exhaust pipe in such amanner that the detected excessive ammonia concentration approacheszero. The system 20 for measuring ammonia concentration will bedescribed in detail below.

As illustrated in FIG. 1, the gas sensor 30 is fixed in the pipe 10 insuch a manner that the central axis of the gas sensor 30 isperpendicular to the flow of the target gas in the pipe 10. The gassensor 30 may be fixed in the pipe 10 in such a manner that the centralaxis of the gas sensor 30 is perpendicular to the flow of the target gasin the pipe 10 and is tilted at a predetermined angle (for example, 45°)with respect to the vertical direction (an up and down direction of FIG.1). As illustrated in the enlarged cross-sectional view of FIG. 1, thegas sensor 30 includes a sensor element 31, a protective cover 32 thatcovers and protects the front end side (the lower end side in FIG. 1) ofthe sensor element 31, which is an end side of the sensor element 31 inthe longitudinal direction, an element fixing portion 33 thatencapsulates and fix the sensor element 31, and a nut 37 fitted to theelement fixing portion 33. The one end side of the sensor element 31 iscovered with a porous protective layer 48.

The protective cover 32 is a cylindrical cover with a closed bottom, thecylindrical cover covering one end of the sensor element 31. Although asingle-layer cover is used in FIG. 1, for example, two-or-more-layercover including an inner protective cover and an outer protective covermay be used. The protective cover 32 has holes through which the targetgas is allowed to flow into the protective cover 32. The one end of thesensor element 31 and the porous protective layer 48 are arranged in acavity surrounded by the protective cover 32.

The element fixing portion 33 includes a cylindrical main metal fitting34, a ceramic supporter 35 encapsulated in an inner through-hole of themain metal fitting 34, and a compact 36 that is encapsulated in theinner through-hole of the main metal fitting 34 and that is formed of aceramic powder composed of, for example, talc. The sensor element 31 islocated on the central axis of the element fixing portion 33 and extendsthrough the element fixing portion 33 in the longitudinal direction. Thecompact 36 is compressed between the main metal fitting 34 and thesensor element 31. Thus, the compact 36 seals the through-hole in themain metal fitting 34 and fixes the sensor element 31.

The nut 37 is fixed coaxially with the main metal fitting 34 and has anexternal thread portion on an outer periphery thereof. The externalthread portion of the nut 37 is fitted with a fitting member 12 that iswelded to the pipe 10 and that has an internal thread portion on aninner periphery thereof. Thus, the gas sensor 30 can be fixed to thepipe 10 while the one end side of the sensor element 31 and theprotective cover 32 protrude into the pipe 10.

The sensor element 31 will be described with reference to FIG. 2. Thecross-sectional view of the sensor element 31 of FIG. 2 illustrates asectional view taken along the central axis of the sensor element 31 inthe longitudinal direction (cross section taken in the up and downdirection of FIG. 1). The sensor element 31 includes a base 40 composedof an oxygen-ion-conducting solid electrolyte, a detection electrode 51and an auxiliary electrode 52 arranged on the side of an end (the lowerend of FIG. 1 and the left end of FIG. 2) of the sensor element 31 andon the upper surface of the base 40, a reference electrode 53 arrangedinside the base 40, and a heater portion 60 that adjusts the temperatureof the base 40.

The base 40 has a plate-like structure in which four layers, i.e., afirst substrate layer 41, a second substrate layer 42, a spacer layer43, and a solid electrolyte layer 44, are stacked, in this order, fromthe bottom in FIG. 2, each of the layers being formed of anoxygen-ion-conducting solid electrolyte layer composed of, for example,zirconia (ZrO₂). A solid electrolyte used to form these four layers is adense, gas-tight material. The periphery of a portion of the base 40 inthe protective cover 32 is exposed to the target gas introduced into theprotective cover 32. A reference gas introduction cavity 46 is providedbetween an upper surface of the second substrate layer 42 and a lowersurface of the solid electrolyte layer 44 in the base 40, a side portionof the cavity being defined by a side surface of the spacer layer 43.The reference gas introduction cavity 46 has an opening portion on theother end side (right end side of FIG. 2) remote from the one end sideof the sensor element 31. For example, air is introduced into thereference gas introduction cavity 46, air serving as a reference gasused to measure ammonia concentration and oxygen concentration. Each ofthe layers of the base 40 may be formed of a substrate containing 3% to15% by mole yttria (Y₂O₃) (yttria-stabilized zirconia (YSZ) substrate)serving as a stabilizer.

The detection electrode 51 is a porous electrode arranged on an uppersurface of the solid electrolyte layer 44 of the base 40 in FIG. 2. Thedetection electrode 51, the solid electrolyte layer 44, and thereference electrode 53 form a mixed potential cell 55. In the mixedpotential cell 55, a mixed potential (electromotive force EMF) isgenerated in the detection electrode 51, depending on the concentrationof a predetermined gas component in the target gas. The value of theelectromotive force EMF between the detection electrode 51 and thereference electrode 53 is used to derive the ammonia concentration inthe target gas. The detection electrode 51 is composed of, as a maincomponent, a material that establishes a mixed potential depending onthe ammonia concentration and that has detection sensitivity to theammonia concentration. The detection electrode 51 may be composed of anoble metal, such as gold (Au), as a main component. The detectionelectrode 51 is preferably composed of a Au—Pt alloy as a maincomponent. The term “main component” used here refers to a componentcontained in a largest amount present (atm %, atomic percent) withrespect to the total amount of components contained. The detectionelectrode 51 preferably has a degree of concentration (=amount of Aupresent [atom %]/amount of Pt present [atom %]) of 0.3 or more, thedegree of concentration being measured by at least one of X-rayphotoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES).A degree of concentration of 0.3 or more can more reliably establish themixed potential. The degree of concentration of the detection electrode51 refers to the degree of surface concentration on a surface of noblemetal particles of the detection electrode 51. The amount of Au present[atom %] is determined as the amount of Au present on the surfaces ofthe noble metal particles of the detection electrode 51. Similarly, theamount of Pt present [atom %] is determined as the amount of Pt presenton the surfaces of the noble metal particles of the detection electrode51. With regard to the surfaces of the noble metal particles, a surface(for example, an upper surface in FIG. 2) of the detection electrode 51or a fracture surface of the detection electrode 51 may be used. Forexample, in the case where the surface (the upper surface in FIG. 2) ofthe detection electrode 51 is exposed, the degree of concentration canbe measured on the surface; hence, the measurement may be performed byXPS. The degree of concentration may also be measured by AES. In thecase where the detection electrode 51 is covered with the porousprotective layer 48 as described in this embodiment, the fracturesurface (fracture surface in the up and down direction of FIG. 2) of thedetection electrode 51 is subjected to measurement by XPS or AES todetermine the degree of concentration. A higher degree of concentrationresults in a smaller amount of Pt present on the surface of thedetection electrode 51, thereby inhibiting the decomposition of ammoniain the target gas around the detection electrode 51 due to Pt. Thus, ahigher degree of concentration results in a more improved derivationaccuracy of the ammonia concentration in the system 20 for measuringammonia concentration. Specifically, the degree of concentration ispreferably 0.1 or more, more preferably 0.3 or more. The upper limit ofthe degree of concentration is not particularly set. For example, thedetection electrode 51 may not contain Pt. The entire detectionelectrode 51 may be composed of Au. The detection electrode 51 has aporosity of, for example, 25% by volume to 60% by volume.

The auxiliary electrode 52 is a porous electrode arranged on the uppersurface of the solid electrolyte layer 44, similarly to the detectionelectrode 51. The auxiliary electrode 52, the solid electrolyte layer44, and the reference electrode 53 form an electrochemical concentrationcell 56. In the concentration cell 56, an electromotive force differenceV, which is a potential difference depending on the difference in oxygenconcentration between the auxiliary electrode 52 and the referenceelectrode 53, is established. The value of the electromotive forcedifference V is used to derive the oxygen concentration (oxygen partialpressure) in the target gas. The auxiliary electrode 52 may be composedof a catalytically active noble metal. For example, Pt, Ir, Rh, Rd, oran alloy containing at least one thereof can be used for the auxiliaryelectrode 52. In this embodiment, the auxiliary electrode 52 is composedof Pt.

The reference electrode 53 is a porous electrode arranged on the lowersurface of the solid electrolyte layer 44, i.e., arranged on a side ofthe solid electrolyte layer 44 opposite that on which the detectionelectrode 51 and the auxiliary electrode 52 are arranged. The referenceelectrode 53 is exposed in the reference gas introduction cavity 46, anda reference gas (here, air) in the reference gas introduction cavity 46is introduced thereinto. The potential of the reference electrode 53 isthe standard for the electromotive force EMF and the electromotive forcedifference V. The reference electrode 53 may be composed of acatalytically active noble metal. For example, Pt, Ir, Rh, Rd, or analloy containing at least one thereof can be used for the referenceelectrode 53. In this embodiment, the reference electrode 53 is composedof Pt.

The porous protective layer 48 covers a surface of the sensor element 31including the detection electrode 51 and the auxiliary electrode 52. Forexample, the porous protective layer 48 serves to inhibit the occurrenceof cracking in the sensor element 31 due to the adhesion of water in thetarget gas. The porous protective layer 48 is composed of, for example,alumina, zirconia, spinel, cordierite, titania, or magnesia as a maincomponent. In this embodiment, the porous protective layer 48 iscomposed of alumina. The thickness of the porous protective layer 48 is,but not particularly limited to, for example, 20 to 1,000 μm. Theporosity of the porous protective layer 48 is, but not particularlylimited to, for example, 5% by volume to 60% by volume. The sensorelement 31 may not include the porous protective layer 48.

The heater portion 60 serves to control the temperature of the base 40(in particular, the solid electrolyte layer 44) by heating and keepingit warm in order to activate the solid electrolyte of the base 40 toincrease the oxygen-ion conductivity. The heater portion 60 includes aheater electrode 61, a heater 62, a through-hole 63, a heater insulatinglayer 64, and a lead wire 66. The heater electrode 61 is an electrodearranged so as to be in contact with a lower surface of the firstsubstrate layer 41. The heater electrode 61 is connected to a heaterpower supply 77 of the apparatus 70 for measuring ammonia concentration.

The heater 62 is an electrical resistor arranged so as to be heldbetween the first substrate layer 41 and the second substrate layer 42.The heater 62 is connected to the heater electrode 61 through the leadwire 66 and the through-hole 63. The heater 62 is fed from the heaterpower supply 77 through the heater electrode 61 to generate heat, sothat the base 40 included in the sensor element 31 is heated and keptwarm. The heater 62 is configured to be able to control the output witha temperature sensor (here, temperature acquisition section 78) in sucha manner that the mixed potential cell 55 and the concentration cell 56(in particular, the solid electrolyte layer 44) have a predeterminedoperating temperature. The operating temperature is preferably 450° C.or higher because the solid electrolyte layer 44 of the mixed potentialcell 55 can be appropriately activated. The operating temperature ispreferably 650° C. or lower because it is possible to inhibit a decreasein the measurement accuracy due to the combustion of ammonia. Theoperating temperature may be 600° C. or lower. The heater insulatinglayer 64 is an insulating layer that is arranged on upper and lowersurfaces of the heater 62 and that is composed of an insulating materialsuch as alumina, specifically porous alumina.

The apparatus 70 for measuring ammonia concentration is an apparatus formeasuring the ammonia concentration in the target gas with the sensorelement 31. The apparatus 70 for measuring ammonia concentration alsoserves as a controller of the sensor element 31. The apparatus 70 formeasuring ammonia concentration includes a control section 72, anelectromotive force acquisition section 75, an oxygen concentrationacquisition section 76, the heater power supply 77, and the temperatureacquisition section 78.

The control section 72 controls the entire apparatus and, for example,is a microprocessor including CPU, RAM, and so forth. The controlsection 72 includes a memory part 73 that stores a processing programand various data sets. The electromotive force acquisition section 75 isa module that acquires information about the electromotive force EMF ofthe mixed potential cell 55. In this embodiment, the electromotive forceacquisition section 75 is connected to the detection electrode 51 andthe reference electrode 53 of the mixed potential cell 55 and thusfunctions as a voltage detection circuit that measures an electromotiveforce EMF. The oxygen concentration acquisition section 76 is a modulethat acquires information about the oxygen concentration in the targetgas. In this embodiment, the oxygen concentration acquisition section 76is connected to the auxiliary electrode 52 and the reference electrode53 of the concentration cell 56 and thus functions as a voltagedetection circuit that measures the electromotive force difference Vserving as information about the oxygen concentration. The electromotiveforce acquisition section 75 and the oxygen concentration acquisitionsection 76 output the electromotive force EMF and the electromotiveforce difference V that have been measured by them to the controlsection 72. The control section 72 derives the ammonia concentration inthe target gas from the electromotive force EMF and the electromotiveforce difference V. The heater power supply 77 is a power supply thatsupplies power to the heater 62, and the output power is controlled bythe control section 72. The temperature acquisition section 78 is amodule that acquires a value about the temperature of the heater 62(here, value of resistance). The temperature acquisition section 78acquires the value of resistance of the heater 62 by, for example,connecting the temperature acquisition section 78 to the heaterelectrode 61, allowing a minute electric current to flow, and measuringa voltage.

Each of the detection electrode 51, the auxiliary electrode 52, and thereference electrode 53 is electrically connected to a corresponding oneof lead wires arranged toward the other end of the sensor element 31(right side of FIG. 2) (not illustrated in FIG. 2). The electromotiveforce acquisition section 75 and the oxygen concentration acquisitionsection 76 measure the electromotive force EMF and the electromotiveforce difference V, respectively, through the lead wires.

The measurement of the ammonia concentration with the system 20 formeasuring ammonia concentration will be described below. FIG. 3 is aflow chart illustrating an example of an ammonia concentrationderivation routine executed by the control section 72. The routine isstored in, for example, the memory part 73 of the control section 72.When a command to derive ammonia concentration is fed from the engineECU 9, the routine is repeatedly executed, for example, with apredetermined period (for example, several milliseconds to several tensof milliseconds). The control section 72 controls, in advance, thetemperature of the mixed potential cell 55 and the concentration cell 56to a predetermined operating temperature (for example, a temperature inthe range of 450° C. or higher and 650° C. or lower) by controlling theoutput power of the heater power supply 77 to produce heat from theheater 62. For example, the control section 72 controls the temperatureof the mixed potential cell 55 and the concentration cell 56 to apredetermined operating temperature by controlling the output power ofthe heater power supply 77 in such a manner that the temperature (here,resistance) of the heater 62 acquired by the temperature acquisitionsection 78 is a predetermined value.

When the ammonia concentration derivation routine is started, thecontrol section 72 executes an electromotive force acquisition step ofacquiring information about the electromotive force EMF of the mixedpotential cell 55 with the electromotive force acquisition section 75(step S100). In this embodiment, the control section 72 acquires thevalue of the electromotive force EMF measured by the electromotive forceacquisition section 75 on an as-is basis. The control section 72executes the ammonia concentration derivation routine in a state inwhich, basically, an exhaust gas from the engine 1 flows through thepipe 10 and the protective cover 32. Thus, the control section 72acquires the electromotive force EMF of the mixed potential cell 55while the detection electrode 51 is exposed to the target gas. Here, inthe mixed potential cell 55, electrochemical reactions, such as theoxidation of ammonia and the ionization of oxygen in the target gas,occur at the triple phase boundary of the detection electrode 51, thesolid electrolyte layer 44 and the target gas to establish a mixedpotential on the detection electrode 51. Thus, the electromotive forceEMF is a value based on the ammonia concentration and the oxygenconcentration in the target gas.

The control section 72 executes an oxygen concentration acquisition stepof acquiring information about oxygen concentration in the target gaswith the oxygen concentration acquisition section 76 (step S110). Inthis embodiment, the control section 72 acquires the electromotive forcedifference V of the concentration cell 56 from the oxygen concentrationacquisition section 76. Here, in the concentration cell 56, theelectromotive force difference V is generated between the auxiliaryelectrode 52 and the reference electrode 53, depending on the differencein oxygen concentration between the target gas and air in the referencegas introduction cavity 46. Hydrocarbons, NH₃, CO, NO, NO₂ in the targetgas are subjected to redox by the catalysis of Pt serving as theauxiliary electrode 52. The concentrations of these gas components inthe target gas are significantly lower than the oxygen concentration inthe target gas. Thus, the occurrence of the redox has little influenceon the oxygen concentration in the target gas. Accordingly, theelectromotive force difference V is a value based on the oxygenconcentration in the target gas. By the control section 72, any one ofstep S100 and step S110 may be first executed, or the steps may beexecuted in parallel.

Subsequently, the control section 72 executes a concentration derivationstep of deriving ammonia concentration in the target gas from theinformation about the electromotive force EMF acquired in step S100, theinformation about the oxygen concentration acquired in step S110, andthe relationship represented by formula (1) (step S120) and terminatesthe routine. The relationship represented by formula (1) is stored in,for example, the memory part 73, in advance.

EMF=α log_(a)(p _(NH3))−β log_(b)(p _(O2))+γ log_(c)(p _(NH3))×γ log_(c)(p _(NH3))×log_(d)(p _(O2)+) B  (1)

(where

EMF: an electromotive force of the mixed potential cell,

α, β, γ, and B: constants (provided that each of α, β, and γ≠0),

a, b, c, and d: any base (provided that each of a, b, c, and d≠1, andeach of a, b, c, and d>0),

p_(NH3): the ammonia concentration in the target gas, and

p_(O2): the oxygen concentration in the target gas).

In step S120, the control section 72 replaces “EMF” in formula (1) bythe value of the electromotive force EMF acquired in step S100. Thecontrol section 72 derives the oxygen concentration p_(O2) from theelectromotive force difference V acquired in step S110 and therelationship, which is stored in the memory part 73 in advance, betweenthe electromotive force difference V and the oxygen concentration p_(O2)and replaces “p_(O2)” in formula (1) by the derived value. The controlsection 72 derives the ammonia concentration p_(NH3) in formula (1). Theunits of the electromotive force EMF may be, for example, [mV]. Theammonia concentration p_(NH3) is the volume fraction of ammonia in thetarget gas. The oxygen concentration p_(O2) is the volume fraction ofoxygen in the target gas. With regard to the units of p_(NH3) andp_(O2), a value given in parts per million [ppm] may be used, a valuegiven in percent [%] may be used, or a dimensionless value (for example,in the case of 10%, the value is 0.1) may be used. p_(NH3) and p_(O2)may be given in different units. Each of the bases a, b, c, and d may bea value of 10 or Napier's constant e. Each of the constants α, β, γ, andB has a value determined, depending on the sensor element 31 and canhave different values, depending on the sensor element 31. The constantsα, β, γ, and B can be determined by, for example, experiments describedbelow, in advance. The constants α and β may satisfy α:β≠(⅔):(½). Theconstants α and β may have a positive value. The constant γ may have apositive value or a negative value. The derivation of the ammoniaconcentration p_(NH3) executed by the control section 72 on the basis ofthe relationship of formula (1) may be performed using the relationshipof formula (1) and is not limited to the derivation of the ammoniaconcentration using formula (1) itself. For example, formula (1) itselfmay be stored in the memory part 73. Formula (1a) or (1b), describedbelow, obtained by modifying the formula (1) may be stored. Formula(1c), described below, obtained by modifying the formula (1a) in such amanner that the left side is “p_(NH3)” alone may be stored. Therelationship of values of the variables (EMF, p_(NH3), and p_(O2)) offormula (1) is stored as a map in the memory part 73. The controlsection 72 may derive the ammonia concentration p_(NH3) from the map.

EMF=(α+γ′ log_(d)(p _(O2)))log_(a)(p _(NH3))−β log_(b)(p _(O2))+B  (1a)

(where γ′=γ/log_(a) c)

EMF=α log_(a)(p _(NH3))−(β−γ″ log_(c)(p _(NH3)))log_(b)(p _(O2))+B  (1b)

(where γ″=γ/log_(b) d)

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 2} \rbrack & \; \\{p_{{NH}\; 3} = {a^{{({{EMF} + {\beta \; {\log_{b}{(p_{02})}}} - B})}/{({\alpha + {\gamma^{\prime}{\log_{d}{(p_{02})}}}})}}( {{{where}\mspace{14mu} \gamma^{\prime}} = \frac{\gamma}{\log_{a}c}} )}} & ( {1c} )\end{matrix}$

As described above, the control section 72 derives the ammoniaconcentration p_(NH3) in the target gas from the relationship of formula(1) in this embodiment. Thus, the ammonia concentration in the targetgas can be derived with high accuracy, compared with, for example, inthe case of using formula (2) described above. This will be describedbelow.

As described above, formula (2) is known as the characteristics of theelectromotive force EMF of the mixed potential-type ammonia sensor.However, the inventors have conducted studies and have found that in anactual sensor element (for example, the sensor element 31), therelationship among the electromotive force EMF, the ammoniaconcentration p_(NH3), the oxygen concentration p_(O2), the H₂Oconcentration p_(H2O) does not obey formula (2). For example, althoughthe relationship between the degree of the effect of the ammoniaconcentration p_(NH3) on the electromotive force EMF (NH₃ sensitivity)and the degree of the effect of the oxygen concentration p_(O2) on theelectromotive force EMF (O₂ interference) should be NH₃ sensitivity:O₂interference=(⅔):(½) from the coefficients of the term p_(NH3) and theterm p_(O2) in the right side of formula (2), the relationship was notobtained, in some cases. According to formula (2), although the effectof the H₂O concentration p_(H2O) on the electromotive force EMF (H₂Ointerference) should be present, in fact, even when the H₂Oconcentration p_(H2O) in the target gas was changed, the electromotiveforce EMF remained substantially unchanged.

With regard to the oxidation of ammonia and the ionization of oxygen inthe target gas, an anodic reaction represented by equation (a) describedbelow and a cathodic reaction represented by equation (b) describedbelow occur at the triple phase boundary of the mixed potential cell 55.Equations (a) and (b) can also be expressed as equations (a)′ and (b)′.In equation (a), “O_(O)” represents an oxygen ion (O²⁻) present in anoxygen site in the solid electrolyte layer 44. The fourth term in theright side of equation (a) indicates that an oxygen ion is not present(not sufficient) in the oxygen site in the solid electrolyte layer 44.

[Math. 3]

[Math. 3]

[Anodic reaction]

⅔NH₃+O_(O)→H₂O+⅓N₂+2e ⁻+V_(O) ^(••)  (a)

NH₃+O₂→H₂O+N₂ +e ⁻  (a)′

[Cathodic reaction]

½O₂+2e ⁻+V_(O) ^(••)→O_(O)  (b)

O₂+4e ⁻→2O²⁻  (b)′

The anodic reaction and the cathodic reaction occur simultaneously atthe triple phase boundary of one detection electrode (for example, thedetection electrode 51) to form a local cell, thereby establishing anelectromotive force EMF. This is a mixed potential cell (for example,the mixed potential cell 55). The electromotive force EMF at this timeshould theoretically obey formula (2). For example, the coefficient “⅔”of the ammonia concentration p_(NH3) in formula (2) is a value based onthe coefficient “⅔” of NH₃ on the left side of equation (a). Similarly,the coefficient “½” of the oxygen concentration p_(O2) in the formula(2) and the coefficient “1” of the H₂O concentration pH₂O are valuesbased on the coefficient “½” of O₂ on the left side of equation (b) andthe coefficient “1” of H₂O on the right side of equation (a),respectively.

For actual sensor elements, however, it was found in experiments thatthe relationship among the variables obeys formula (1), and not formula(2). The inventors have considered that the reason for this thatp_(NH3), p_(O2), and p_(H2O) in formula (2) need not be replaced by theconcentrations in the target gas and should be replaced by partialpressures at the triple phase boundary. Letting an NH₃ partial pressure,an O₂ partial pressure, and a H₂O partial pressure at the triple phaseboundary on the detection electrode be p_(NH3)*, p_(O2)*, and p_(H2O)*,respectively, formula (A1) holds. This can also be derived from formula(2). The actual electromotive force EMF seemingly obeys formula (A1),and not formula (2). Because p_(NH3)*, p_(O2)*, and p_(H2O)* at thetriple phase boundary cannot be directly detected, a formula includingp_(NH3), p_(O2), and p_(H2O) in the target gas need to be derived fromformula (A1). The inventors thought that we could explain below thatformula (1) including p_(NH3), p_(O2), and p_(H2O) holds on the basis offormula (A1).

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 4} \rbrack & \; \\{{EMF} \propto {\frac{RT}{2F}( {{\frac{2}{3}\ln \; p_{{NH}\; 3}^{*}} - {\frac{1}{2}\ln \; p_{O\; 2}^{*}} - {\ln \; p_{H\; 2O}^{*}}} )}} & ({A1})\end{matrix}$

Let us first consider a mixed potential equation from a microscopicpoint of view. As described above, the partial pressures, ln p_(NH3)*,ln p_(O2)*, and ln p_(H2O)*, at the triple phase boundary on thedetection electrode are not equal to the partial pressures, ln p_(NH3),ln p_(O2), and ln p_(H2O), in an atmospheric gas (target gas). This isbecause the following dynamic changes occur in the electrochemicalreactions: molecules are adsorbed onto a surface of the detectionelectrode, diffused on the surface of the detection electrode to reachthe triple phase boundary, and subjected to electrochemical reactions,and the resulting products are desorbed from the surface of thedetection electrode, rather than the fact that the molecules directlyreach the triple phase boundary from the gas phase. Let us now considerthe product H₂O formed in the anodic reaction. The formed H₂O isseemingly adsorbed on the detection electrode and then desorbed into thegas phase. Because a large amount of H₂O is present in the target gas,the H₂O formed in the anodic reaction seems to be not readily desorbedfrom the surface of the detection electrode. It is thus considered thatthe H₂O partial pressure p_(H2O)* at the triple phase boundary duringthe adsorption of H₂O is larger than the H₂O partial pressure p_(H2O) inthe target gas and that formula (A2) described below always holds. Inthe target gas (here, an exhaust gas), the H₂O concentration is usuallyabout 5% to about 15%, and the total pressure remains constant at 1 atm.For the sake of safety, considering that the H₂O concentration changesin a wide range of 1% to 20%, formula (A3) described below holds.

p_(H2O)*>p_(H2O)  (A2)

0.01 atm<p_(H2O)<0.2 atm  (A3)

Let us next consider that what will become of p_(H2O)* when p_(H2O) ischanged while H₂O is adsorbed on the surface of the detection electrode.With regard to H₂O at the triple phase boundary, H₂O adsorbed on thedetection electrode is denoted by H₂O(ad), and H₂O in the gas phase isdenoted by H₂O(gas). The partial pressure of H₂O adsorbed on thedetection electrode is denoted by p_(H2O(ad)), and the partial pressureof H₂O in the gas phase is denoted by p_(H2O(gas)). Thus,p_(H2O)*=p_(H2O(ad))+p_(H2O(gas)). p_(H2O(ad)) includes the partialpressure of H₂O that comes from the target gas and that is adsorbed onthe detection electrode, and the partial pressure of H₂O that is formedby the anodic reaction (the foregoing equations (a) and (a)′) and thatis adsorbed on the detection electrode. p_(H2O(gas)) includes thepartial pressure of H₂O that is contained in the target gas and that ispresent at the triple phase boundary in a gas phase state, and thepartial pressure of H₂O that is formed by the anodic reaction and thatis in a gas phase state. With regard to H₂O(ad) and H₂O(gas), formulae(A4) and (A5) described below hold, provided that an equilibriumconstant K=(constant). Although p_(H2O)* is supposed to be changedaccording to formulae (A4) and (A5), in fact, it behaves differently.The reason for this is presumably that p_(H2O) changes in the rangerepresented by formula (A3) described above, whereas p_(H2O(ad)) cannotchange once the adsorption of H₂O on the detection electrode isstabilized and reaches a steady state (=1 atm). The reason p_(H2O(ad))is 1 atm in the steady state is described below. Because H₂O_((ad))adsorbed on the detection electrode is not in the gas phase, the amountof H₂O(ad) is expressed as activity a_(H2O(ad)), and not as partialpressure, to be exact. When H₂O(ad) is regarded as a solid, the activitya_(H2O(ad)) have a value of 1 (i.e., the activity is 1 irrespective ofthe amount adsorbed on the detection electrode), and an activity of 1can be regarded as comparable to a partial pressure of 1 atm.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 5} \rbrack & \; \\{{H_{2}{O({ad})}}\overset{K}{leftarrows}{H_{2}{O({gas})}}} & ({A4}) \\{K = {\frac{p_{H\; 2{O{({ad})}}}}{p_{H\; 2{O{({gas})}}}} = \frac{p_{H\; 2O}^{*} - p_{H\; 2{O{({gas})}}}}{p_{H\; 2{O{({gas})}}}}}} & ({A5})\end{matrix}$

Accordingly, p_(H2O(ad)) can be regarded as 1 atm. Although as withformula (A3), p_(H2O(gas)) seems to be about 0.01 to about 0.2 atm,because H₂O(ad), which can be regarded as 1 atm, is present on thesurface of the detection electrode, H₂O in the gas phase is less likelyto contribute to the reaction, the partial pressure p_(H2O(gas)) of H₂Opresent in the gas phase at the triple phase boundary seems to have avalue significantly smaller than 0.01 to 0.2 atm. Thus,p_(H2O(ad))>>p_(H2O(gas)) seemingly holds, and p_(H2O(gas)) seems tohave a very small, negligible value. Accordingly, even if p_(H2O)changes while H₂O is adsorbed on the surface of the detection electrode,p_(H2O)* can be regarded as constant, as represented by formula (A6).Thus, formula (A1) can be regarded as formula (A7). That is, the H₂Opartial pressure p_(H2O)* at the triple phase boundary can be regardedas having no effect (H₂O interference) on the electromotive force EMF.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 6} \rbrack & \; \\{p_{H\; 2O}^{*} = {{p_{H\; 2{O{({ad})}}} + p_{H\; 2{O{({gas})}}}}\underset{\mspace{11mu} \cdot}{\overset{\cdot \mspace{11mu}}{=}}{p_{H\; 2{O{({ad})}}} = {{constant}\mspace{14mu} ( {1\mspace{14mu} {atm}} )}}}} & ({A6}) \\{{EMF} \propto {\frac{RT}{2F}( {{\frac{2}{3}\ln \; p_{{NH}\; 3}^{*}} - {\frac{1}{2}\ln \; p_{O\; 2}^{*}}} )}} & ({A7})\end{matrix}$

Let us then consider a mixed potential equation from a macroscopic pointof view. When the total pressure of the target gas is 1 atm, theconcentration is equal to the partial pressure; thus, p_(NH3), p_(O2),and p_(H2O) will be explained below as partial pressures. Formula (A8)can be derived from formula (A3). Formula (A9) can be derived fromformula (A6). From formulae (A8) and (A9), formula (A10) holds. Lettingthe ratio of ln p_(H2O)* to ln p_(H2O) be a pressure adjustment factorδ, δ is defined by formula (A11). From formula (A10), δ satisfies−1<δ<1. Similarly, letting the ratio of ln p_(NH3)* to ln p_(NH3) be apressure adjustment factor δ′, δ′ is defined by formula (A12). Thepressure adjustment factors δ and δ′ are values characteristic of thesensor element, depending on, for example, the composition and thestructure of the detection electrode.

−4.6<ln p _(H2O)<−1.6  (A8)

ln p_(H2O)*≠0  (A9)

|ln p_(H2O)*|<|ln p_(H2O)|  (A10)

δ=ln p _(H2O) */ln p _(H2O)  (A11)

δ′=ln p _(NH3) */ln p _(NH3)  (A12)

Formula (A1) is transformed using the pressure adjustment factors δ andδ′ to derive formula (A13). Formula (A13) is obtained by substituting lnp_(H2O)*=δ×ln p_(H2O) obtained from formula (A11), ln p_(NH3)*=δ×lnp_(NH3) obtained from formula (A12), and ln p_(O2)*=ln p_(O2) in formula(A1). In existing O₂ sensors and SOFCs, it is well known that therelationship between the oxygen concentration and the electromotiveforce obeys the Nernst equation; hence, it is clear that ln p_(O2)*=lnp_(O2) holds.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 7} \rbrack & \; \\{{EMF} \propto {\frac{RT}{2F}( {{\frac{2}{3}\delta^{\prime}\ln \; p_{{NH}\; 3}} - {\frac{1}{2}\ln \; p_{O\; 2}} - {{\delta ln}\; p_{H\; 2O}}} )}} & ({A13})\end{matrix}$

From formulae (A6) and (A11), ln p_(H2O)*=δ×ln p_(H2O)=0 holds. Thus,formula (A13) can be expressed as formula (A14). Formula (A14) can beexpressed as formula (A15). The constants A and B are valuescharacteristic of the sensor element, depending on, for example, thecomposition and the structure of the detection electrode. In formula(A15), letting the base of the logarithm be freely selected values a andb and letting the coefficients of the terms in the right side beconstants α and β, formula (A16) described below is derived.

$\begin{matrix}\lbrack {{Math}.\mspace{14mu} 8} \rbrack & \; \\{{EMF} \propto {\frac{RT}{2F}( {{\frac{2}{3}\delta^{\prime}\ln \; p_{{NH}\; 3}} - {\frac{1}{2}\ln \; p_{O\; 2}}} )}} & ({A14}) \\{{EMF} \propto {{A\frac{RT}{2F}( {{\frac{2}{3}\delta^{\prime}\ln \; p_{{NH}\; 3}} - {\frac{1}{2}\ln \; p_{O\; 2}}} )} + {B( {{where}\mspace{14mu} A\mspace{14mu} {and}\mspace{14mu} B\mspace{14mu} {are}\mspace{14mu} {constants}} )}}} & ({A15}) \\{{EMF} = {{\alpha \; {\log_{a}( p_{{NH}\; 3} )}} - {\beta \; {\log_{b}( p_{02} )}} + B}} & ({A16})\end{matrix}$

Unlike formula (2), formula (A16) can express the fact that therelationship, p_(NH3) sensitivity:p_(O2) sensitivity=(⅔):(½), does notalways hold and that substantially no H₂O interference is present. Thus,the use of formula (A16) can derive the ammonia concentration p_(NH3)with high accuracy, compared with formula (2).

The inventors have conducted further studies and have found thefollowing: According to formula (A16), the relationship between theammonia concentration p_(NH3) and the electromotive force EMF will be alinear one with a slope of the constant α, and the constant α will notvary as the oxygen concentration p_(O2) is changed; however, in fact,the constant α varies depending on the oxygen concentration p_(O2). Forexample, a higher oxygen concentration p_(O2) had a tendency to lead toa steeper slope of a straight line expressing the relationship betweenthe ammonia concentration p_(NH3) and the electromotive force EMF, insome cases. Furthermore, it was also found that the relationship betweenthe logarithm of the oxygen concentration p_(O2) and the slope of thestraight line expressing the relationship between the ammoniaconcentration p_(NH3) and the electromotive force EMF is one expressedby a straight line (linear function). Thus, the relationship wasreflected in formula (A16) to derive formula (1a), and formula (1a) wastransformed to derive formula (1). Formula (1) corresponds to a formulaobtained by the addition of the term “γlog_(c)(p_(NH3))×log_(d)(p_(O2))” to formula (A16). This term isaffected by both of the ammonia concentration p_(NH3) and the oxygenconcentration p_(O2) and is thus referred to as an “interaction term”.The use of formula (1) can derive the ammonia concentration p_(NH3) withhigher accuracy than that in the case of using formula (A16).

An exact reason the interaction term affects the electromotive force EMFis not clear. However, the interaction term seemingly expresses theoccurrence of the gas-phase combustion of ammonia and oxygen before thetarget gas reaches the triple phase boundary. For example, it isbelieved that because each of the porous protective layer 48 and thedetection electrode 51 is a porous material, when the target gas passesthrough pores of at least one of them, ammonia molecules collide withoxygen molecules to burn. A larger amount of ammonia burned reduceslarger amounts of ammonia and oxygen before ammonia and oxygen in thetarget gas reach the triple phase boundary; thus, ammonia and oxygen inthe target gas seemingly have less effect on the electromotive forceEMF. The interaction term seems to express an increase or a decrease inelectromotive force EMF depending on the amount burned.

The constant γ in the interaction term is a value characteristic of thesensor element, depending on, for example, structures of pores (forexample, the porosity and the pore size) of each of the porousprotective layer and the detection electrode, and the presence orabsence of the porous protective layer. In the case where theinteraction term correlates with the combustion of ammonia, the constantγ of the interaction term can vary depending on the operatingtemperature of the mixed potential cell. For example, a higher operatingtemperature can result in a larger absolute value of the constant γ.

Formulae (A16) and (1) are not limited to the case where the target gashas a total pressure of 1 atm, and can also be applied to the case wherethe total pressure is about 1 atm (for example, 0.9 atm to 1.10 atm).Formulae (A16) and (1) can also be applied to the case where the totalpressure of the target gas is not about 1 atm. The temperature of thetarget gas to which formula (1) is applied may be, but is notparticularly limited to, 150° C. or higher or 200° C. or higher. Thetemperature of the target gas may be 400° C. or lower.

The constants α, β, γ, and B in formula (1) can be determined byexperiments as described below, in advance. FIG. 4 is a flow chartillustrating an example of constant derivation processing. In theconstant derivation processing, the sensor element 31, which is a targetwith the constants to be derived, is subjected to first electromotiveforce measurement processing for acquiring first electromotive forcedata multiple times, the first electromotive force data expressing thecorrespondence between the ammonia concentration p_(NH3) and theelectromotive force EMF (step S200). Specifically, the correspondencebetween the ammonia concentration p_(NH3) and the electromotive forceEMF is acquired as the first electromotive force data by exposing thesensor element 31 to the target gas with the oxygen concentration p_(O2)and the ammonia concentration p_(NH3) that have been adjusted topredetermined values and measuring the electromotive force EMF. Next,first electromotive force data sets are similarly acquired by measuringthe electromotive force EMF multiple times at different ammoniaconcentrations p_(NH3) in the target gas while the oxygen concentrationp_(O2) in the target gas remains unchanged (constant). Subsequently, aswith the first electromotive force measurement processing, electromotiveforce EMF measurement processing that is executed multiple times atdifferent ammonia concentrations p_(NH3) while the oxygen concentrationp_(O2) remains unchanged (constant) is executed multiple times atdifferent oxygen concentrations p_(O2) (second to nth electromotiveforce measurement processing) to acquire the second to the nthelectromotive force data sets (step S210). n represents an integer of 2or more. For example, only the second electromotive force measurementprocessing may be executed in step S210.

Next, the slope K (here, K1) and the intercept L (here, L1) of formula(3) described below are derived from the first electromotive force datasets acquired in step S200 (step S220). In the case where formula (1a)described above is regarded as a linear function of the electromotiveforce EMF and the logarithm of the ammonia concentration p_(NH3), i.e.,log_(a)(p_(NH3)), the slope K and the intercept L are defined byformulae (3) and (4), respectively, and formula (1a) can thus beexpressed by formula (5). As is clear from formulae (3) and (4), each ofthe slope K and the intercept L is constant at a constant oxygenconcentration p_(O2); hence, on the basis of the first electromotiveforce data sets (data sets at a constant oxygen concentration p_(O2)),the slope K (K1) and the intercept L (L1) corresponding to the oxygenconcentration p_(O2) at the time of the measurement of the data sets canbe derived. Specifically, the slope and the intercept obtained when therelationship between the logarithm of the ammonia concentration p_(NH3),log_(a)(p_(NH3)), and the electromotive force EMF in the firstelectromotive force data sets acquired by executing the firstelectromotive force measurement processing multiple times isapproximated by a straight line (linear function) are derived as theslope K1 and the intercept L1. The approximation is performed on thebasis of, for example, the method of least squares. Subsequently, aswith step S220, the slopes K2 to Kn and the intercepts L2 to Ln arederived (step S230) in the same way as the slope K1 and the intercept L1on the basis of the second to the nth electromotive force data setsacquired in step S210.

K=α+γ′ log _(d)(p _(O2))  (3)

L=−β log _(b)(p _(O2))+B  (4)

EMF=K×log_(a)(p _(NH3))+L  (5)

Subsequently, the constants α and γ′ are derived from formula (3)described above (step S240) on the basis of the correspondences betweenthe slopes K (K1 to Kn) derived in steps S220 and S230 and the oxygenconcentrations p_(O2) at the time of the derivation of the slopes K1 toKn (for example, in the cases of the slope K1, the oxygen concentrationp_(O2) at the time of the first electromotive force data measurement).As is clear from formula (3), the slope K is a linear function of thelogarithm of the oxygen concentration p_(O2), i.e., log_(d)(p_(O2)).When the relationship between the log_(d)(p_(O2)) and the slope K isapproximated by a straight line (linear function), the slope is derivedas the constant γ′, and the intercept is derived as the constant α. Byderiving the constant γ′, the constant γ can be derived (see the provisoof formula (1a)). When base a=base c, constant γ′=constant γ.

As with the step S240, the constants β and B are derived from formula(4) on the basis of the correspondences between the intercepts L (L1 toLn) derived in steps S220 and S230 and the oxygen concentrations p_(O2)at the time of the derivation of the intercepts L1 to Ln (for example,in the cases of the intercept L1, the oxygen concentration p_(O2) at thetime of the first electromotive force data measurement) (step S250). Asis clear from formula (4), the intercept L is a linear function of thelogarithm of the oxygen concentration p_(O2), i.e., log_(b)(p_(O2)).When the relationship between the log_(b)(p_(O2)) and the intercept L isapproximated by a straight line (linear function), the slope is derivedas the constant β, the intercept is derived as the constant B. Thereby,the constants α, β, γ, and B are derived, and this processing iscompleted.

Each of the first to the nth electromotive force data sets describedabove is measured in a state in which the mixed potential cell 55 isheated with the heater 62 to a predetermined fixed operatingtemperature. Comparisons between formula (1) and formula (A15) revealthat the constants α and β vary depending on the temperature T of themixed potential cell 55, i.e., the operating temperature of the sensorelement 31 in use. Thus, in the case where one sensor element 31 can beused at different operating temperatures, the constants α and β informula (1) are derived at each of the different operating temperaturesand stored in, for example, the memory part 73, in advance. When thecontrol section 72 executes the ammonia concentration derivationprocessing, the constants α and β corresponding to the operatingtemperature of the sensor element 31 are used. The constant γ can varydepending on the operating temperature of the mixed potential cell 55 asdescribed above; thus, a value corresponding to the operatingtemperature of the mixed potential cell 55 is derived and stored in, forexample, the memory part 73, in advance. The constant B can also varydepending on the operating temperature of the sensor element 31 in use;thus, the constant B may be derived at each of the different operatingtemperatures and stored in, for example, the memory part 73, in advance.

A method other than the foregoing constant derivation processing may beemployed as long as the constants α, β, γ, and B can be derived. Forexample, in step S200, the electromotive force EMF may be measuredmultiple times at different oxygen concentrations p_(O2) in the targetgas while the ammonia concentration p_(NH3) is constant (the same istrue for step S210). The constant derivation processing is not limitedto the case where the electromotive force EMF is measured multiple timeswhile one of the ammonia concentration p_(NH3) and the oxygenconcentration p_(O2) is constant and the other is changed. Theelectromotive forces EMFs may be measured with at least four targetgases in which at least one of the ammonia concentration p_(NH3) and theoxygen concentration p_(O2) is different when the sensor element 31 isexposed to each of the target gases. If at least four correspondences(electromotive force data sets) among the electromotive forces EMFs, theoxygen concentrations p_(O2), and the ammonia concentrations p_(NH3) arethus acquired, simultaneous equations are solved by replacing variablesin formula (1) by the values of the electromotive force data sets, sothat the constants α, β, γ, and B can be derived. Like the foregoingconstant derivation processing, however, the constants are preferablyderived from the electromotive force data sets as many as possible.

Let us now clarify the correspondence between the constituent elementsof this embodiment and constituent elements of the present invention.The solid electrolyte layer 44 of this embodiment corresponds to a solidelectrolyte body of the present invention. The detection electrode 51corresponds to a detection electrode. The reference electrode 53corresponds to a reference electrode. The mixed potential cell 55corresponds to a mixed potential cell. The electromotive forceacquisition section 75 corresponds to a electromotive force acquisitionsection. The oxygen concentration acquisition section 76 corresponds toan oxygen concentration acquisition section. The control section 72corresponds to an ammonia concentration derivation section. In thisembodiment, an example of a method for measuring ammonia concentrationof the present invention is also described by explaining the operationof the apparatus 70 for measuring ammonia concentration.

According to the system 2 for treating an exhaust gas described above indetail, in the apparatus 70 for measuring ammonia concentration, the useof the relationship of formula (1) can derive the ammonia concentrationin the target gas with higher accuracy than that in the case of usingformula (2) described above.

The target gas may have a temperature of 150° C. or higher. Thederivation of the ammonia concentration p_(NH3) using the relationshipof formula (1) is suitable even for a high-temperature target gas.

Because the detection electrode 51 is composed of the Au—Pt alloy as amain component, the mixed potential is easily established at the triplephase boundary of the solid electrolyte layer 44 and the target gas. Thedetection electrode 51 has a degree of concentration of 0.3 or more,which is measured by at least one of XPS and AES, and thus enables themixed potential to be more reliably established.

Because the operating temperature of the mixed potential cell 55 is 450°C. or higher, the solid electrolyte layer 44 can be appropriatelyactivated. Because the operating temperature of the mixed potential cell55 is 650° C. or lower, a decrease in measurement accuracy due to thecombustion of ammonia can be inhibited.

The system 2 for treating an exhaust gas includes the one or moreoxidation catalysts (DOC 4 and ASC 8) arranged in the exhaust gas path3, and the sensor element 31 is arranged on the downstream side of theexhaust gas path 3 in contrast to the DOC 4, which is one of the one ormore oxidation catalysts, arranged at the upstream end. Thus, the targetgas in which a component (for example, at least one of hydrocarbons andcarbon monoxide) that is present in the target gas and that affects themeasurement accuracy of the ammonia concentration has been oxidized bythe oxidation catalysts reaches the sensor element 31. Accordingly, inthe system 2 for treating an exhaust gas, the ammonia concentration inthe target gas can be derived with higher accuracy.

The present invention is not limited to the above-described embodiment,and can be carried out by various modes as long as they belong to thetechnical scope of the invention.

For example, in the foregoing embodiment, although the detectionelectrode 51 and the reference electrode 53 are arranged on the solidelectrolyte layer 44, the solid electrolyte layer 44 is not necessarilyused, and they may be arranged on a solid electrolyte body. For example,the detection electrode 51 and the reference electrode 53 may bearranged on upper and lower surfaces of a solid electrolyte bodyincluding solid electrolyte layers stacked. In the foregoing embodiment,although the reference electrode 53 serves as both of the referenceelectrode of the mixed potential cell 55 and the reference electrode ofthe concentration cell 56, this structure is not necessarily used, andthe mixed potential cell 55 and the concentration cell 56 may includedifferent reference electrodes.

In the foregoing embodiment, although the sensor element 31 includes theconcentration cell 56 and thus can measure the oxygen concentration,this structure is not necessarily used. The sensor element 31 may notinclude the concentration cell 56 (specifically, the auxiliary electrode52). In this case, the apparatus 70 for measuring ammonia concentrationmay acquire information about the oxygen concentration from other thanthe sensor element 31. For example, the apparatus 70 for measuringammonia concentration may acquire information about the oxygenconcentration from another sensor that is arranged in the exhaust gaspath 3 and that can detect information about the oxygen concentration(for example, an oxygen sensor, an A/F sensor, or a NOx sensor). Theapparatus 70 for measuring ammonia concentration may acquire informationabout the oxygen concentration from another device (such as the engineECU 9) other than sensors. In the case where the apparatus 70 formeasuring ammonia concentration acquires information about the oxygenconcentration from another sensor arranged at a position of the exhaustgas path 3, the position being different from that of the sensor element31, the apparatus 70 for measuring ammonia concentration preferablyderives the ammonia concentration in consideration of a measurement timelag (time lag C) the difference in position between the sensor element31 and due to the another sensor attached. Specifically, letting thelength of time that the target gas flow from the position of one,located upstream, of the sensor element 31 and the another sensor to theposition of the other in the exhaust gas path 3 be the time lag C, theapparatus 70 for measuring ammonia concentration preferably derives theammonia concentration in consideration of the time lag C. For example,in the case where the another sensor is located on the upstream side ofthe sensor element 31, the control section 72 allows the memory part 73to store the values of oxygen concentration acquired from the anothersensor every predetermined period during the time lag C. Every time theelectromotive force EMF is acquired from the sensor element 31, thecontrol section 72 reads the oldest value of oxygen concentration atthat time (=value acquired in the past by the time lag C) from thememory part 73 and derives the ammonia concentration from the acquiredelectromotive force EMF, the value of the oxygen concentration read, andformula (1). In this way, the apparatus 70 for measuring ammoniaconcentration can derive the ammonia concentration with higher accuracyby considering the time lag C.

Although the engine 1 is a diesel engine in the foregoing embodiment, agasoline engine may be used.

In the foregoing embodiment, although the apparatus 70 for measuringammonia concentration is an apparatus different from the engine ECU 9,the apparatus 70 for measuring ammonia concentration may be part of theengine ECU 9.

EXAMPLES

Examples in which a method for measuring ammonia concentration wasspecifically performed will be described below as Examples. The presentinvention is not limited to Examples described below.

Production of Sensor Element 1

A sensor element to be used for the measurement of ammonia concentrationwith an apparatus for measuring ammonia concentration was produced. Fourceramic green sheets containing a ceramic component composed of azirconia solid electrolyte containing 3% by mole yttria serving as astabilizer were prepared as the layers of the base 40. For example,sheet holes used for positioning during printing and stacking andthrough-holes required were formed in the green sheets. A space to beformed into the reference gas introduction cavity 46 was formed in thegreen sheet to be formed into the spacer layer 43 by, for example,punching, in advance. Various patterns were formed by pattern printingon the ceramic green sheets corresponding to the first substrate layer41, the second substrate layer 42, the spacer layer 43, and the solidelectrolyte layer 44, and the resulting ceramic green sheets weresubjected to drying treatment. Specifically, for example, patterns forthe detection electrode 51 composed of the Au—Pt alloy, the auxiliaryelectrode 52 and the reference electrode 53 composed of Pt, lead wires,and the heater portion 60 were formed. The pattern printing wasperformed by applying pattern-forming pastes to the green sheets using aknown screen printing technique, each of the pattern-forming pastesbeing prepared to provide characteristics required for a correspondingone of the target objects. After the pattern printing and the dryingwere completed, printing and drying treatment of a bonding paste tostack and bond the green sheets corresponding to the layers togetherwere performed. Compression bonding treatment was performed in which thegreen sheets including the bonding paste were stacked in a predeterminedorder while the green sheets were positioned with the sheet holes, andthe resulting stack were subjected to compression bonding underpredetermined temperature and pressure conditions to form a laminate.Laminated pieces having the same size as the sensor element 31 were cutfrom the resulting laminate. The cut laminated pieces were fired with atubular furnace at 1,100° C. for 2 hours in an air atmosphere, therebyproviding the sensor elements 31 each including the detection electrode51, the auxiliary electrode 52, and the reference electrode 53 that werearranged on the solid electrolyte layer 44. The sensor elements 31 weresubjected to dipping with an alumina-containing slurry and firing toform the porous protective layers 48 on surfaces of the sensor elements31. In this way, the sensor element 31 was produced and was referred toas a sensor element 1. The degree of concentration on the surface of anoble metal on the fracture surface of the detection electrode 51 in thesensor element 1 was measured by AES and found to be 0.99. The detectionelectrode 51 had a porosity of 45% by volume. The porous protectivelayer 48 had a porosity of 40% by volume. In the following tests, theoperating temperature of the sensor element 1 in use was 480° C.

[Experiment 1: Acquisition of Electromotive Force Data Sets]

The sensor element 1 was subjected to steps S200 and S210 in theconstant derivation processing to acquire first to sixth electromotiveforce data sets (13 for each data set). The first electromotive forcedata was acquired by measuring the electromotive forces EMFs [mV] at afixed oxygen concentration p_(O2) of 1%, a fixed H₂O concentrationp_(H2O) of 5%, and different ammonia concentrations p_(NH3), as listedin Table 1, in a target gas. A component (base gas) other than theforegoing components in the target gas was nitrogen, and the temperaturewas 200° C. The target gas was allowed to flow through the pipe having adiameter of 70 mm at a flow rate of 200 L/min. The second to the sixthelectromotive force data sets were measured as in the firstelectromotive force data, except that the oxygen concentration p_(O2)(fixed value) in the target gas was changed as listed in Table 1. Table1 lists the ammonia concentrations p_(NH3), the oxygen concentrationsp_(O2), and the electromotive forces EMFs of the first to the sixthelectromotive force data sets measured. FIG. 5 is a graph depicting therelationship between the ammonia concentration p_(NH3) [ppm] and theelectromotive force EMF [mV] of the sensor element 1 (first to sixthelectromotive force data sets). The horizontal axis of FIG. 5 is on alogarithmic scale. FIG. 5 indicates that the relationships between thelogarithms of the ammonia concentrations p_(NH3) at fixed oxygenconcentrations p_(O2) and the electromotive forces EMFs can beapproximated by a straight line. The results indicated that higheroxygen concentrations p_(O2) resulted in higher slopes K of the straightlines and that higher oxygen concentrations p_(O2) resulted in lowerintercepts L of the straight lines. The results also indicated that theratio of the NH₃ sensitivity to the O₂ interference in the measuredvalues of the electromotive force EMF was not always (⅔):(½). Theseresults indicated that the relationship among the electromotive forceEMF, the ammonia concentration p_(NH3), and the oxygen concentrationp_(O2) was not matched to formula (2).

TABLE 1 First Second Third Fourth Fifth Sixth electromotiveelectromotive electromotive electromotive electromotive electromotiveforce data force data force data force data force data force data p_(O2)= 1% p_(O2) = 3% p_(O2) = 5% p_(O2) = 10% p_(O2) = 15% p_(O2) = 20%p_(NH3)[ppm] EMF[mV] EMF[mV] EMF[mV] EMF[mV] EMF[mV] EMF[mV] 25 241.850210.583 195.600 168.633 152.050 133.750 50 266.217 238.567 224.333204.550 187.783 177.417 100 290.133 265.967 262.200 238.650 225.700216.350 300 330.183 312.467 304.617 298.050 290.250 284.333 500 359.783346.433 341.917 341.667 336.800 332.200 750 374.767 362.800 360.567362.733 358.917 355.583 1000 373.600 371.967 373.867 376.900 369.883369.600 1 142.917 90.817 56.233 21.467 9.833 1.667 3 182.983 143.367119.083 84.017 55.233 31.650 5 196.833 159.933 138.467 111.200 85.88366.933 10 216.133 182.033 162.683 140.300 118.900 103.367 25 249.083217.117 200.700 182.100 163.600 151.983 50 268.500 238.500 222.883206.400 188.733 178.200

[Experiment 2: Derivation of Slope K and Intercept L]

Subsequently, steps S220 and S230 in the constant derivation processingwere executed to derive the slopes K (K1 to K6) and the intercepts L (L1to L6) in the first to the sixth electromotive force data sets. Forexample, with regard to the approximate straight line at an oxygenconcentration p_(O2) of 1% (first electromotive force data) illustratedin FIG. 5, the slope was defined as K1 (=34.67), and the intercept wasdefined as L1 (=137.92). The intercept L1 is a value of theelectromotive force EMF when log_(a)(p_(NH3)) of the approximatestraight line is zero, in other words, when p_(NH3) is 1 ppm. Table 2lists the derived slopes K, the derived intercepts L, and the oxygenconcentrations p_(O2) corresponding thereto. FIG. 6 is a graph depictingthe relationship between the oxygen concentration p_(O2) and the slope Klisted in Table 2. FIG. 7 is a graph depicting the relationship betweenthe oxygen concentration p_(O2) and the intercept L listed in Table 2.The horizontal axis of each of FIGS. 6 and 7 is on a logarithmic scale.FIG. 6 indicates that the relationship between the logarithm of theoxygen concentration p_(O2) and the slope K can be approximated by astraight line. FIG. 7 indicates that the relationship between thelogarithm of the oxygen concentration p_(O2) and the intercept L can beapproximated by a straight line.

TABLE 2 p_(O2)[%] Slope K Intercept L First electromotive 1 34.670137.920 force data Second electromotive 3 40.086 89.489 force data Thirdelectromotive 5 44.462 58.546 force data Forth electromotive 10 50.26619.795 force data Fifth electromotive 15 52.981 −5.359 force data Sixthelectromotive 20 55.316 −25.029 force data

[Experiment 3: Derivation of Constants α, β, γ, and B]

Steps S240 and S250 in the constant derivation processing were executedon the basis of the data sets obtained in experiments 1 and 2 to derivethe constants α, β, γ, and B of the sensor element 1. Specifically,formula (6) described below was derived as an approximate straight lineexpressing the relationship between the logarithm of the oxygenconcentration p_(O2) and the slope K illustrated in FIG. 6. The constantγ′=7.09 and the constant α=33.636 were derived from formula (6). Formula(7) described below was derived as an approximate straight lineexpressing the relationship between the logarithm of the oxygenconcentration p_(O2) and the intercept L illustrated in FIG. 7. Theconstant β=54.69 and the constant B=143.55 were derived from formula(7). In a formula derived here, each of the bases a to d in formula (1)was Napier's constant e. Thus, γ=γ′=7.09 was derived.

K=7.09×ln(p _(O2))+33.636  (6)

L=−54.69×ln(p _(O2))+143.55  (7)

From experiments 1 to 3 described above, formula (8) expressing therelationship among the variables (EMF, p_(NH3), and p_(O2)) in thesensor element 1 was derived. In formula (8), the units of theelectromotive force EMF are [mV], the units of the ammonia concentrationp_(NH3) are [ppm], and the units of the oxygen concentration p_(O2) are[%].

EMF=33.636×ln(p _(NH3))−54.69×ln(p _(O2))+7.09×ln(p _(NH3))×ln(p_(O2))+143.55  (8)

[Verification Test]

The electromotive forces EMFs corresponding to ammonia concentrationsp_(NH3) and oxygen concentrations p_(O2) were derived from formula (8)under the same conditions as those in the first to the sixthelectromotive force data sets. Table 3 lists the results. FIG. 8 is agraph illustrating six straight lines represented by a formula (formulacorresponding to formula (5)) derived from formula (8) at the differentoxygen concentrations p_(O2) used in the first to the sixthelectromotive force data sets. FIG. 8 also illustrates the points of thefirst to the sixth electromotive force data sets (measured values)illustrated in FIG. 5. FIG. 8 and comparisons between Tables 1 and 3indicated that the measured values of the electromotive forces EMFs werematched to the electromotive forces EMFs derived from formula (8) withgood accuracy. That is, although the relationship among theelectromotive force EMF, the ammonia concentration p_(NH3), and theoxygen concentration p_(O2) based on actual measurement was notexpressed by formula (2) as illustrated in FIG. 5, the relationshipbased on the measured values was able to be expressed by formula (8)derived from formula (1). These results indicated that the use offormula (1) was able to derive the ammonia concentration p_(NH3) withhigher accuracy than that in the case of using formula (2).

TABLE 3 p_(O2) = 1% p_(O2) = 3% p_(O2) = 5% p_(O2) = 10% p_(O2) = 15%p_(O2) = 20% p_(NH3)[ppm] EMF[mV] EMF[mV] EMF[mV] EMF[mV] EMF[mV]EMF[mV] 1 143.550 83.467 55.530 17.622 −4.553 −20.287 3 180.503 128.977105.019 72.510 53.493 40.001 5 197.685 150.138 128.030 98.031 80.48368.033 10 221.000 178.852 159.254 132.662 117.106 106.069 25 251.820216.809 200.530 178.441 165.520 156.352 50 275.135 245.523 231.754213.071 202.143 194.389 100 298.450 274.237 262.979 247.702 238.766232.426 300 335.402 319.747 312.468 302.590 296.812 292.713 500 352.585340.908 335.479 328.112 323.802 320.745 750 366.223 357.704 353.744348.369 345.225 342.995 1000 375.899 369.622 366.703 362.742 360.425358.782

The electromotive forces EMFs of the sensor element 1 were measured withtarget gases having a constant ammonia concentration p_(NH3) of 100 ppm,a constant oxygen concentration p_(O2) of 10%, and different H₂Oconcentrations p_(H2O) of 1% to 12% as listed in Table 4. Conditionsother than those described above were the same as in experiment 1. FIG.9 is a graph depicting the relationship between the H₂O concentrationp_(H2O) [%} and the electromotive force EMF [mV] of the sensor element1. FIG. 9 indicated that the electromotive force EMF remains almostunchanged at different H₂O concentrations p_(H2O) in the target gases(substantially no H₂O interference). That is, the results indicated thatthe term of the H₂O concentration p_(H2O) in formula (2) was not matchedto the relationship between the electromotive force EMF and the H₂Oconcentration p_(H2O) actually measured.

TABLE 4 p_(H2O)[%] EMF[mV] 1 238.65 3 238.65 5 238.65 10 238.65 12235.65

The present application claims priority from U.S. provisional PatentApplication No. 62/411,736 filed on Oct. 24, 2016 and Japanese PatentApplication No. 2017-117089 filed on Jun. 14, 2017, the entire contentsof which are incorporated herein by reference.

What is claimed is:
 1. An apparatus for measuring ammonia concentrationin a target gas with a sensor element including a mixed potential cellthat includes a solid electrolyte body, a detection electrode arrangedon the solid electrolyte body, and a reference electrode arranged on thesolid electrolyte body, the apparatus comprising: an electromotive forceacquisition section configured to acquire information about anelectromotive force of the mixed potential cell while the detectionelectrode is exposed to the target gas; an oxygen concentrationacquisition section configured to acquire information about oxygenconcentration in the target gas; and an ammonia concentration derivationsection configured to derive the ammonia concentration in the target gasfrom the acquired information about the electromotive force, theacquired information about the oxygen concentration, and a relationshiprepresented by formula (1):EMF=α log_(a)(p _(NH3))−β log_(b)(p _(O2))+γ log_(c)(p _(NH3))×log_(d)(p_(O2))+B  (1) (where EMF: an electromotive force of the mixed potentialcell, α, β, γ, and B: constants (provided that each of α, β, and γ≠0),a, b, c, and d: any base (provided that each of a, b, c, and d≠1, andeach of a, b, c, and d>0), p_(NH3): the ammonia concentration in thetarget gas, and p_(O2): the oxygen concentration in the target gas). 2.A system for measuring ammonia concentration, comprising: the apparatusfor measuring ammonia concentration according to claim 1; and the sensorelement.
 3. The system for measuring ammonia concentration according toclaim 2, wherein the detection electrode is composed of a Au—Pt alloy asa main component.
 4. The system for measuring ammonia concentrationaccording to claim 3, wherein the detection electrode has a degree ofconcentration (=amount of Au present [atom %]/amount of Pt present [atom%]) of 0.3 or more, the degree of concentration being measured by atleast one of X-ray photoelectron spectroscopy (XPS) and Auger electronspectroscopy (AES).
 5. The system for measuring ammonia concentrationaccording to claim 2, wherein the sensor element includes a heaterconfigured to heat the mixed potential cell to an operating temperatureof 450° C. or higher and 650° C. or lower.
 6. A system for treating anexhaust gas, comprising: the system for measuring ammonia concentrationaccording to claim 2; and an exhaust gas path through which an exhaustgas serving as the target gas from an internal combustion engine flows,the sensor element being arranged in the exhaust gas path.
 7. The systemfor treating an exhaust gas according to claim 6, further comprising:one or more oxidation catalysts arranged in the exhaust gas path,wherein the sensor element is arranged on the downstream side of theexhaust gas path in contrast to one of the one or more oxidationcatalysts arranged at an upstream end.
 8. A method for measuring ammoniaconcentration in a target gas with a sensor element including a mixedpotential cell that includes a solid electrolyte body, a detectionelectrode arranged on the solid electrolyte body, and a referenceelectrode arranged on the solid electrolyte body, the method comprising:an electromotive force acquisition step of acquiring information aboutan electromotive force of the mixed potential cell while the detectionelectrode is exposed to the target gas; an oxygen concentrationacquisition step of acquiring information about oxygen concentration inthe target gas; and a concentration derivation step of deriving theammonia concentration in the target gas from the acquired informationabout the electromotive force, the acquired information about the oxygenconcentration, and a relationship represented by formula (1):EMF=α log_(a)(p _(NH3))−β log_(b)(p _(O2))+γ log_(c)(p _(NH3))×log_(d)(p_(O2))+B  (1) (where EMF: an electromotive force of the mixed potentialcell, α, β, γ, and B: constants (provided that each of α, β, and γ≠0),a, b, c, and d: any base (provided that each of a, b, c, and d≠1, andeach of a, b, c, and d>0), p_(NH3): the ammonia concentration in thetarget gas, and p_(O2): the oxygen concentration in the target gas).